{"schema":"vela.problem-packet.v0.1","problem":395,"statement":"If $z_1,\\ldots,z_n\\in \\mathbb{C}$ with $\\lvert z_i\\rvert=1$ then is it true that the probability that\\[\\lvert \\epsilon_1z_1+\\cdots+\\epsilon_nz_n\\rvert \\leq \\sqrt{2},\\]where $\\epsilon_i\\in \\{-1,1\\}$ uniformly at random, is $\\gg 1/n$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}